Progress in Mathematics

Getz, Jayce; Goresky, Mark

In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adèlic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.

Details

Published by: Birkhäuser

Publication Date: 2012-03-30

Format: Hardcover

ISBN-13: 9783034803502

DOI: 10.1007/978-3-0348-0351-9

Dimensions: 235cm x155cm

Pages: 258